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<div class="subTitle">org.apache.commons.math3.analysis.polynomials</div>
<h2 title="Class PolynomialFunctionLagrangeForm" class="title">Class PolynomialFunctionLagrangeForm</h2>
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<dt>All Implemented Interfaces:</dt>
<dd><a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a></dd>
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<pre>public class <span class="strong">PolynomialFunctionLagrangeForm</span>
extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a>
implements <a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a></pre>
<div class="block">Implements the representation of a real polynomial function in
 <a href="http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html">
 Lagrange Form</a>. For reference, see <b>Introduction to Numerical
 Analysis</b>, ISBN 038795452X, chapter 2.
 <p>
 The approximated function should be smooth enough for Lagrange polynomial
 to work well. Otherwise, consider using splines instead.</p></div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>1.2</dd></dl>
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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionLagrangeForm.html#PolynomialFunctionLagrangeForm(double[],%20double[])">PolynomialFunctionLagrangeForm</a></strong>(double[]&nbsp;x,
                              double[]&nbsp;y)</code>
<div class="block">Construct a Lagrange polynomial with the given abscissas and function
 values.</div>
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<td class="colFirst"><code>protected void</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionLagrangeForm.html#computeCoefficients()">computeCoefficients</a></strong>()</code>
<div class="block">Calculate the coefficients of Lagrange polynomial from the
 interpolation data.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionLagrangeForm.html#degree()">degree</a></strong>()</code>
<div class="block">Returns the degree of the polynomial.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionLagrangeForm.html#evaluate(double[],%20double[],%20double)">evaluate</a></strong>(double[]&nbsp;x,
        double[]&nbsp;y,
        double&nbsp;z)</code>
<div class="block">Evaluate the Lagrange polynomial using
 <a href="http://mathworld.wolfram.com/NevillesAlgorithm.html">
 Neville's Algorithm</a>.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionLagrangeForm.html#getCoefficients()">getCoefficients</a></strong>()</code>
<div class="block">Returns a copy of the coefficients array.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionLagrangeForm.html#getInterpolatingPoints()">getInterpolatingPoints</a></strong>()</code>
<div class="block">Returns a copy of the interpolating points array.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionLagrangeForm.html#getInterpolatingValues()">getInterpolatingValues</a></strong>()</code>
<div class="block">Returns a copy of the interpolating values array.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionLagrangeForm.html#value(double)">value</a></strong>(double&nbsp;z)</code>
<div class="block">Calculate the function value at the given point.</div>
</td>
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<td class="colFirst"><code>static boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionLagrangeForm.html#verifyInterpolationArray(double[],%20double[],%20boolean)">verifyInterpolationArray</a></strong>(double[]&nbsp;x,
                        double[]&nbsp;y,
                        boolean&nbsp;abort)</code>
<div class="block">Check that the interpolation arrays are valid.</div>
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<h4>PolynomialFunctionLagrangeForm</h4>
<pre>public&nbsp;PolynomialFunctionLagrangeForm(double[]&nbsp;x,
                              double[]&nbsp;y)
                               throws <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
                                      <a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a>,
                                      <a href="../../../../../../org/apache/commons/math3/exception/NonMonotonicSequenceException.html" title="class in org.apache.commons.math3.exception">NonMonotonicSequenceException</a></pre>
<div class="block">Construct a Lagrange polynomial with the given abscissas and function
 values. The order of interpolating points are not important.
 <p>
 The constructor makes copy of the input arrays and assigns them.</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - interpolating points</dd><dd><code>y</code> - function values at interpolating points</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the array lengths are different.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></code> - if the number of points is less than 2.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NonMonotonicSequenceException.html" title="class in org.apache.commons.math3.exception">NonMonotonicSequenceException</a></code> - if two abscissae have the same value.</dd></dl>
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<h4>value</h4>
<pre>public&nbsp;double&nbsp;value(double&nbsp;z)</pre>
<div class="block">Calculate the function value at the given point.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html#value(double)">value</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>z</code> - Point at which the function value is to be computed.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the function value.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>x</code> and <code>y</code> have
 different lengths.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NonMonotonicSequenceException.html" title="class in org.apache.commons.math3.exception">NonMonotonicSequenceException</a></code> - if <code>x</code> is not sorted in strictly increasing order.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></code> - if the size of <code>x</code> is less
 than 2.</dd></dl>
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<a name="degree()">
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<h4>degree</h4>
<pre>public&nbsp;int&nbsp;degree()</pre>
<div class="block">Returns the degree of the polynomial.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the degree of the polynomial</dd></dl>
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<h4>getInterpolatingPoints</h4>
<pre>public&nbsp;double[]&nbsp;getInterpolatingPoints()</pre>
<div class="block">Returns a copy of the interpolating points array.
 <p>
 Changes made to the returned copy will not affect the polynomial.</p></div>
<dl><dt><span class="strong">Returns:</span></dt><dd>a fresh copy of the interpolating points array</dd></dl>
</li>
</ul>
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<h4>getInterpolatingValues</h4>
<pre>public&nbsp;double[]&nbsp;getInterpolatingValues()</pre>
<div class="block">Returns a copy of the interpolating values array.
 <p>
 Changes made to the returned copy will not affect the polynomial.</p></div>
<dl><dt><span class="strong">Returns:</span></dt><dd>a fresh copy of the interpolating values array</dd></dl>
</li>
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<h4>getCoefficients</h4>
<pre>public&nbsp;double[]&nbsp;getCoefficients()</pre>
<div class="block">Returns a copy of the coefficients array.
 <p>
 Changes made to the returned copy will not affect the polynomial.</p>
 <p>
 Note that coefficients computation can be ill-conditioned. Use with caution
 and only when it is necessary.</p></div>
<dl><dt><span class="strong">Returns:</span></dt><dd>a fresh copy of the coefficients array</dd></dl>
</li>
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<a name="evaluate(double[], double[], double)">
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<h4>evaluate</h4>
<pre>public static&nbsp;double&nbsp;evaluate(double[]&nbsp;x,
              double[]&nbsp;y,
              double&nbsp;z)
                       throws <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
                              <a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a>,
                              <a href="../../../../../../org/apache/commons/math3/exception/NonMonotonicSequenceException.html" title="class in org.apache.commons.math3.exception">NonMonotonicSequenceException</a></pre>
<div class="block">Evaluate the Lagrange polynomial using
 <a href="http://mathworld.wolfram.com/NevillesAlgorithm.html">
 Neville's Algorithm</a>. It takes O(n^2) time.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - Interpolating points array.</dd><dd><code>y</code> - Interpolating values array.</dd><dd><code>z</code> - Point at which the function value is to be computed.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the function value.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if <code>x</code> and <code>y</code> have
 different lengths.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NonMonotonicSequenceException.html" title="class in org.apache.commons.math3.exception">NonMonotonicSequenceException</a></code> - if <code>x</code> is not sorted in strictly increasing order.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></code> - if the size of <code>x</code> is less
 than 2.</dd></dl>
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<h4>computeCoefficients</h4>
<pre>protected&nbsp;void&nbsp;computeCoefficients()</pre>
<div class="block">Calculate the coefficients of Lagrange polynomial from the
 interpolation data. It takes O(n^2) time.
 Note that this computation can be ill-conditioned: Use with caution
 and only when it is necessary.</div>
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<a name="verifyInterpolationArray(double[], double[], boolean)">
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<h4>verifyInterpolationArray</h4>
<pre>public static&nbsp;boolean&nbsp;verifyInterpolationArray(double[]&nbsp;x,
                               double[]&nbsp;y,
                               boolean&nbsp;abort)
                                        throws <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
                                               <a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a>,
                                               <a href="../../../../../../org/apache/commons/math3/exception/NonMonotonicSequenceException.html" title="class in org.apache.commons.math3.exception">NonMonotonicSequenceException</a></pre>
<div class="block">Check that the interpolation arrays are valid.
 The arrays features checked by this method are that both arrays have the
 same length and this length is at least 2.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - Interpolating points array.</dd><dd><code>y</code> - Interpolating values array.</dd><dd><code>abort</code> - Whether to throw an exception if <code>x</code> is not sorted.</dd>
<dt><span class="strong">Returns:</span></dt><dd><code>false</code> if the <code>x</code> is not sorted in increasing order,
 <code>true</code> otherwise.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the array lengths are different.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NumberIsTooSmallException.html" title="class in org.apache.commons.math3.exception">NumberIsTooSmallException</a></code> - if the number of points is less than 2.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NonMonotonicSequenceException.html" title="class in org.apache.commons.math3.exception">NonMonotonicSequenceException</a></code> - if <code>x</code> is not sorted in strictly increasing order and <code>abort</code>
 is <code>true</code>.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionLagrangeForm.html#evaluate(double[],%20double[],%20double)"><code>evaluate(double[], double[], double)</code></a>, 
<a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionLagrangeForm.html#computeCoefficients()"><code>computeCoefficients()</code></a></dd></dl>
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